What is the cross product of the vectors (1, 2, 3) and (4, 5, 6)?
Correct Answer: (-3, 6, -3)
- Step 1: Write down the vectors. We have vector A = (1, 2, 3) and vector B = (4, 5, 6).
- Step 2: Set up the determinant for the cross product using the unit vectors i, j, k. It looks like this: |i j k| |1 2 3| |4 5 6|.
- Step 3: Calculate the determinant. This involves finding the components of the resulting vector.
- Step 4: For the i component, calculate: (2*6 - 3*5) = (12 - 15) = -3.
- Step 5: For the j component, calculate: (3*4 - 1*6) = (12 - 6) = 6. Remember to put a negative sign in front of this component, so it becomes -6.
- Step 6: For the k component, calculate: (1*5 - 2*4) = (5 - 8) = -3.
- Step 7: Combine the components to get the final result: (-3, -6, -3).
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